Bragg grating cavities embedded into nano-photonic waveguides for Purcell enhanced quantum dot emission

1. Introduction

The advances achieved in solid-state based technologies and integrated nanophotonics bring compact quantum technology based devices within reach in the near future [1–3]. Particularly, single photons which are very robust carriers of quantum information are a key element for a wide range of applications ranging from secure communication to sensing, metrology and computational tasks [4–8].

Semiconductor quantum dots (QDs) have been proven as excellent non-classical light sources as they provide single-photons with outstanding optical properties [9]. The relatively easy integration within III-V semiconductor chips, especially in combination with more complex systems (e.g. waveguides, photonic crystals) is particularly appealing and fully compatible with several proposals for integrated quantum devices that are based on the efficient generation, guiding, manipulation and detection of single photons on an individual chip [8,10,11].

The integration of QDs in gallium arsenide (GaAs) based waveguide structures e.g. ridge waveguides, photonic crystal (PhC) waveguides, nanobeam waveguides seems one of the most promising approaches for on-chip quantum optics experiments [10,12–14]. It was shown that not only the efficient generation e.g. resonant fluorescence [15–17] of single photons is possible but also the on-chip manipulation is feasible [10,18–21]. Furthermore, the on-chip detection of single photons via superconducting nanowire single photon detectors (SNSPDs) integrated in waveguides structures was already demonstrated [22–24].

Free standing waveguides (PhC- and nanobeam waveguides) have a large refractive index contrast resulting in large photon coupling efficiencies (>95 %) into a single guided mode [14,25]. Also a simultaneous Purcell enhancement (>5) of the QD emission was demonstrated in PhC waveguides [26–28]. However, complex underetching steps are needed for this types of waveguides. The resulting structures are fragile and typically in the tens of micrometer range. Common experimental mechanical instabilities or vibrations can either lead to a destruction of the waveguides or reducing the optical properties of the emitted photons [10,29]. Ideas to overcome this problems are heterogeneous approaches combining III V materials with silicon-on-insulator technology or silicon nitride (Si₃N₄) [30]. Further ideas−are the use of transition regions from a freestanding waveguide to a ridge waveguide or the covering with a cladding material [29,31]. However, the results are either complex multi-step fabrication routines or the introduction of further losses in the presence of transition regions.

The mentioned problems can be avoided with the direct integration of QDs into ridge waveguides as they provide a high mechanical stability with a centimeter range footprint in combination with low propagation losses [10,12,32]. The disadvantage is the small refractive index contrast for GaAs / AlGaAs based waveguides leading to low directional photon coupling efficiencies between 9 % to 15 % [12,33].

Here, we present a cavity design based on a Bragg grating that can be directly integrated into a ridge waveguide making underetching steps, transition regions or complex covering steps unnecessary. Finite-difference time-domain (FDTD) simulations [34] show a significant increase of the coupling efficiency to the fundamental waveguide mode with an additional Purcell enhancement. We fabricated several Bragg grating cavities and performed low-temperature micro-photoluminescence and time-correlated single photon counting (TCSPC) experiments on integrated InAs QDs. A subsequent comparison of the measured data with FDTD simulations is carried out and show a good agreement between experiments and simulations.

2. Fabrication and simulations

The sample was grown via metal-organic vapor-phase epitaxy (MOVPE) using an exactly oriented (100)-GaAs substrate. The layer structure consists of a 2 µm thick Al₇₀Ga₃₀As cladding layer followed by a 310 nm GaAs core layer. The GaAs waveguide is designed to guide only the fundamental TE- and TM-mode (w = 470 nm, h = 310 nm) and can be seen in Fig. 1(a). A layer of single self-assembled InAs QDs located at the vertical electrical field maximum of the fundamental TE-mode was included during growth. The period of the grating was chosen to satisfy the Bragg condition Λ = λ_QD / (2 · n_eff) with λ_QD the wavelength of the QD emission and n_eff the effective refractive index of the fundamental TE-mode. The optimum grating period Λ was found via FDTD simulations and is in the range of 140 nm to 145 nm for the wavelength region of interest. The dimension of the cavity and the electrical field profile can be seen in Fig. 1(b–c). The cavity was chosen to be 2Λ corresponding to a one lambda cavity resulting in a maximum field intensity in the center of the cavity region with an exponential decay towards the outside.

 

Fig. 1 (a) Schematic illustration of the waveguide design. (b) Schematic illustration of the integrated Bragg grating cavity and specific parameters. (c) Top view of the simulated electrical field intensity of the cavity mode.

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A scanning electron microscope (SEM) image of the final device can be seen in Fig. 2(a). The grating and the waveguide structure were fabricated with standard electron beam lithography and transferred into the substrate via inductively coupled plasma reactive ion etching (ICP-RIE). We used a two-stage fabrication process for the realization of the structures. Initially, we patterned and etched the Bragg gratings relatively to gold markers into the planar sample surface. The waveguides were subsequently patterned and etched after an repetitive alignment to the gold markers on top of the previously structured grating. The lateral dimensions of the grating were chosen to be 430 nm which is slightly smaller compared to the waveguide dimensions (w = 470 nm). FDTD simulations show that this has no influence on the device performance and leads to a strongly reduced sidewall roughness comparable to a standard waveguide without grating and thus minimizing scattering losses. The transition region between the ridge waveguide and the grating region can be seen in Fig. 2(b). A further benefit of this design is the insusceptibility for alignment errors which are typically in the range of ±25 nm for electron beam lithography.

 

Fig. 2 (a) Perspective view of the cavity region. The inset shows a top view of the cavity with the measured period Λ and the cavity dimensions. (b) Perspective view of the transition region of the waveguide and the integrated Bragg grating. (c) Schematic illustration of the measurement setup with the investigated locations 1–3.

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Simulations show that an asymmetric cavity design with 400 grating periods on the left and 150 on the right side of the central cavity region with an etching depth of t = 70 nm gave the best combined results (Q-factor, β_dir, F_P). Here, right side refers to the side directly facing the cleaved facet of the sample while left side corresponds to the far side of the facet (see Fig. 2(c)). With this design, a simulated Q-factor of 4.8 × 10³ with a corresponding Purcell factor of 20 could be achieved. As the used asymmetric cavity design breaks the propagation symmetry, a preferred emission into only one of the counter-propagating waveguide modes is expected. Therefore, the directional coupling factor β_dir which considers only the spontaneous emission rate into either the left propagating waveguide mode Γ_L or the right propagating waveguide mode Γ_R needs to be considered and is given by

After fabrication, the sample was cleaved perpendicular to the waveguides, placed in a liquid helium flow cryostat and cooled to 4 K. An illustration of the measurement setup can be seen in Fig. 2(c) which allows for the optical excitation on different waveguide positions and the simultaneous observation of the QD emission from the cleaved waveguide facet. A Ti:Sapphire laser emitting at 800 nm was used for wetting layer excitation either in continuous wave (cw) or pulsed operation mode depending on the performed measurements.

3. Results

We fabricated and investigated several Bragg grating cavities utilizing three different designs with 250/250 periods, 300/300 periods and one asymmetric design with 400/150 periods in which the 150 periods directly face the cleaved facet of the sample. In these measurements, we used the QD ensemble at high excitation powers as an internal light source and measured the transmission at the waveguide facet for different excitation locations (see Fig. 2(c) and Fig. 3(a)). The positions are marked as loc 1, loc 2, loc 3 and correspond to the excitation of QDs in a reference WG, in the grating region and directly in the cavity, respectively. For the reference WG (loc 1) the emission of the QD ensemble ranging from around 890 nm to 910 nm can be detected and lies within the typical wavelength range for the used InAs QDs. If the excitation spot is subsequently moved to a waveguide with a Bragg grating (loc 2), the QD emission can still be detected but a clear region with no transmitted QD light is visible. This region corresponds to the stopband of the Bragg grating with a spectral width of around 9 nm. A direct excitation on the cavity (loc 3) leads to the observation of a characteristic peak in the stopband center corresponding to the fundamental resonance of the cavity mode. The Q-factor can then directly extracted from the transmission spectra via Q = ν / Δν and it is shown in Fig. 3(b) for the previously mentioned cavity geometries.

 

Fig. 3 (a) Transmission spectra for different excitation locations on the chip. (b) Measured Q-factor for different numbers of grating periods. (c) Simulated Q-factor dependency for different etching depth t.

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The measured Q-factors are in the range between 2500 and 4600 which is slightly lower compared to the values obtained from FDTD simulations. The small difference between the simulation and the measured values can be attributed to scattering effects due to surface roughness coming from the etching process, material absorption or surface recombination at the GaAs-air interface. A further increase of the Q-factor is expected by depositing a thin layer of Al₂O₃ via atomic layer deposition (ALD) which decrease the losses due to surface absorption as observed e.g. for disk resonators [38]. This can also have a beneficial effect for the reduction of spectral diffusion and linewidth of the QD [39].

The simulated Q-factor of the cavity is dependent on the etching depth t of the grating and shows a bi-Gaussian distribution with optimal values between 60 nm and 90 nm (see Fig. 3(c)). This can be explained with the low refractive index contrast between the waveguide core layer (GaAs) and the bottom cladding layer (AlGaAs) resulting in a preferred radiation into the substrate for a too strong light confinement. As the etching depth of the fabricated gratings were slightly larger as designed (t_design = 70 nm; t_fabr = 100 nm) a further increase of the Q-factor can be expected after an adjustment of the etching depth.

Furthermore, we extracted the spectral position of the cavity resonance from the transmission measurements which can be seen in Fig. 4(a). Here, we found a wavelength correlation which we attributed to the alignment process. If the Bragg grating waveguides were aligned in the center of the gold markers we found an average resonance wavelength of 901.31 nm ± 0.11 nm over the full fabricated chip whereas for cavities that were aligned on the left side or on the right side of the markers we found values of 900.49 nm ± 0.17 nm and 901.93 nm ± 0.38 nm respectively (see Fig. 4(a)). We concluded, that an adjustment of the electron beam lithography in the center of the markers leads to a more accurate alignment and reduced fabrication deviations compared to an alignment outside of the markers. This behavior need to be considered for future application but the vanishing wavelength deviation of only ± 0.11 nm over the complete fabricated chip for waveguides in between the markers indicates the robustness of this cavity design against fabrication imperfections. Therefore, the measured low wavelength tolerance makes the here used cavity particularly suitable for deterministic alignment procedures on preselected QDs were a matching of the QD emission with the cavity resonance is crucial [33,40,41].

 

Fig. 4 (a) Position dependent resonance wavelength for different Bragg cavities (bottom). Illustration of the alignment process relative to gold markers (top). (b) Transmission spectra of a single QD emission line in perfect resonance with the cavity mode.

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If the excitation power is reduced, single emission lines from QDs can be investigated. In Fig. 4(b) a QD emission line spectrally located in the stopband and perfectly matching the cavity resonance is shown. While it is well transmitted through the grating, emission lines of other QDs lying spectrally outside of the resonance are strongly suppressed. This behavior shows the full functionality of the device as a wavelength selective Bragg grating.

A degradation of the linewidth can be a problem according to literature due to the coupling to surface states or charge traps in the presence of etched surfaces [42, 43]. As the measured linewidth of 52 µeV for above-bandgap excitation from the QD in the cavity region in Fig. 4(b) is typical for the here used InAs QDs in bulk we concluded that the etching process has no influence on the linewidth.

As a next step we performed time-resolved µPL measurements on single QDs to verify the enhancement of the spontaneous emission rate via cavity quantum electrodynamic effects (cQED). For this, we investigated QDs that spectrally matched the cavity resonance and were spatially located in the cavity region (loc 3). Here, the Ti:Sapphire laser was used in pulsed operation mode and the quantum dot light was detected with a single photon counting module (SPCM) with a timing jitter of ∼ 40 ps. All TCSPC measurements were performed at low excitation powers well below the saturation level of the QDs.

As a first step, we investigated nearly 20 QD either in reference WGs or far off the cavity beneath the Bragg grating (loc 1, loc 2) to determine an average decay time of the QDs. The measured decay times can be seen in Fig. 5(a). For QDs in the reference WGs (loc 1) we measured values (after deconvolution with the instrumental response function (IRF)) between 700 ps and 1200 ps. This is in good agreement with those obtained from literature and also corresponds to the typical decay times for InAs QDs in GaAs bulk material [44]. Based upon the measured data, we concluded that the fabricated waveguides have no detrimental effect on the QDs. We calculated an average decay time in the reference WGs of τ_{loc 1} = 958 ps ± 128 ps. We performed the same procedure for QDs in the grating region of Bragg grating waveguides far away from the cavity region to ensure that the cavity has no influence on the QDs. Here we obtained an average lifetime of τ_{loc 2} = 852 ps ± 130 ps which indicates that the etched grating has also no or merely a little influence on the spontaneous emission rate. In contrast, for QDs located in the cavity (loc 3), we found a strong modification of the spontaneous emission rate with measured lifetimes as low as 258 ps ± 2 ps (see Table 1). Fig. 5(b) shows the time-resolved µPL trace of such a QD in the cavity in comparison to the QD with the lowermost measured lifetime from the reference WGs. Considering the average lifetime of all measured QDs outside of the cavity as τ_avg = 902 ps ± 137 ps, we get a Purcell enhancement (F_P = τ_avg / τ) of 3.5 ± 0.5.

 

Fig. 5 (a) Measured decay time of more than 20 QDs located at different waveguide positions. (b) Comparison of two measured TCSPC experiments of a QD in a cavity and a reference QD.

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Table 1. Measured decay times and calculated Purcell enhancement of three quantum dots spatially located in the cavity region. The average decay time of all investigated QDs were taken into account for the calculation of the Purcell factor.

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Taking the measured Q-factors of around 3600 into account with the simulated mode volume of V_m ≈ 15 (λ/n)³ we calculated a maximum achievable Purcell enhancement of F_P = 18. The difference between simulation and experiment can be related to a spectral and spatial mismatch of the QD or a misorientation of the dipole [45]. Summarized, we found three QDs showing a non-negligible Purcell enhancement between 2 and 3.5 (see Table 1) with an average Purcell enhancement of 2.72 ± 0.38. For deterministically placed cavities around preselected QDs we would expected a even further Purcell enhancement due to a better spatial overlap with the cavity mode.

4. Conclusion

In conclusion, we have demonstrated the realization of high Q-factor resonators based on Bragg gratings that can be directly and easily integrated into a standard ridge waveguide. The fabrication do not rely on complex underetching steps and can be realized on large scales. Measurements show the robustness of this cavity design against fabrication variations making them fully compatible with state-of-the-art deterministic fabrication processes. We verified with TCSPC experiments the reduction of the lifetime of integrated QDs up to a factor of 3.5 ± 0.5 demonstrating clear Purcell enhancement. The easy scalability in combination with the substantial enhancement of the spontaneous emission rate shows a major step towards large scale on-chip quantum photonic circuits.